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A204018 Symmetric matrix based on f(i,j)=1+max(j mod i, i mod j), by antidiagonals.

%I A204018 #7 Dec 25 2023 18:18:43
%S A204018 1,2,2,2,1,2,2,3,3,2,2,3,1,3,2,2,3,4,4,3,2,2,3,4,1,4,3,2,2,3,4,5,5,4,
%T A204018 3,2,2,3,4,5,1,5,4,3,2,2,3,4,5,6,6,5,4,3,2,2,3,4,5,6,1,6,5,4,3,2,2,3,
%U A204018 4,5,6,7,7,6,5,4,3,2,2,3,4,5,6,7,1,7,6,5,4,3,2,2,3,4,5,6,7,8,8
%N A204018 Symmetric matrix based on f(i,j)=1+max(j mod i, i mod j), by antidiagonals.
%C A204018 A204018 represents the matrix M given by f(i,j)=max{1+(j mod i), 1+( i mod j)} for i>=1 and j>=1.  See A204019 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.
%e A204018 Northwest corner:
%e A204018 1 2 2 2 2 2
%e A204018 2 1 3 3 3 3
%e A204018 2 3 1 4 4 4
%e A204018 2 3 4 1 5 5
%e A204018 2 3 4 5 1 6
%e A204018 2 3 4 5 6 1
%t A204018 f[i_, j_] := 1 + Max[Mod[i, j], Mod[j, i]];
%t A204018 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204018 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A204018 Flatten[Table[f[i, n + 1 - i],
%t A204018   {n, 1, 15}, {i, 1, n}]]   (* A204018 *)
%t A204018 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204018 c[n_] := CoefficientList[p[n], x]
%t A204018 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204018 Table[c[n], {n, 1, 12}]
%t A204018 Flatten[%]                  (* A204019 *)
%t A204018 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204018 Cf. A204019, A204016, A202453.
%K A204018 nonn,tabl
%O A204018 1,2
%A A204018 _Clark Kimberling_, Jan 11 2012